Thermodynamic optimization of quantum algorithms: On-the-go erasure of qubit registers

TL;DR

This paper explores thermodynamic costs of erasing quantum registers during computation, proposing optimal protocols for on-the-go erasure to improve quantum algorithm efficiency and resource management.

Contribution

It introduces new protocols for thermodynamic erasure of quantum registers, balancing memory optimization and algorithm simplification in quantum computing.

Findings

Optimal erasure protocols for Abelian hidden subgroup algorithms

Trade-off between partial information and qubit reduction

Explicit protocols for on-the-go erasure and algorithm simplification

Abstract

We consider two bottlenecks in quantum computing: limited memory size and noise caused by heat dissipation. Trying to optimize both, we investigate "on-the-go erasure" of quantum registers that are no longer needed for a given algorithm: freeing up auxiliary qubits as they stop being useful would facilitate the parallelization of computations. We study the minimal thermodynamic cost of erasure in these scenarios, applying results on the Landauer erasure of entangled quantum registers. For the class of algorithms solving the Abelian hidden subgroup problem, we find optimal on-the-go erasure protocols. We conclude that there is a trade-off: if we have enough partial information about a problem to build efficient on-the-go erasure, we can use it to instead simplify the algorithm, so that fewer qubits are needed to run the computation in the first place. We provide explicit protocols for these two approaches.